The buckling and post-buckling of a film/substrate bilayer, which is often idealised as a coated hyperelastic half space, has received much attention in recent decades due to applications
ranging from cell patterning [1]}, optical gratings [2]}, [3]}, [4]}, and creation of surfaces with desired wetting and adhesion properties [5]}, [6]}, [7]}, to the deduction of material properties of ultrathin films [8]}, [9]}. Under the framework of nonlinear elasticity, early studies include the linear analyses by [10]}, [11]}, [12]}, [13]}, [14]}, and the nonlinear post-buckling analysis by [15]}. More recent studies have addressed the phenomenon of period doubling [16]}, effects of pre-stretching in the half-space [17]}, compressibility [18]}, [19]}, multi-layering [20]}, [21]}, [22]}, growth [23]}, [24]}, [25]}, and magnetorheology [26]}. There also exists a large body of literature based on various approximate models for the layer and substrate; see, e.g., [27]}, [28]}, [29]}, [30]}, and the references therein.
